Flexible couplings



July 8, 1958 c. w. BELDEN ET AL 2,841,966

FLEXIBLE COUPLINGS Original Filed Oct. 30, 1950 5 Sheets-Sheet 1 July 8,1958 c. w. BELDEN ET AL 2,841,966

FLEXIBLE COUPLINGS Original Filed Oct. 50, 1950 5 Sheets-Sheet 2INVENTORS Y B Ar/eg /6)7 0/7%/0p BY Char/e: Wfle/Q en ATTOFIVEK July 8,1958 c. w. BELDEN ET AL FLEXIBLE COUPLINGS 5 Sheets-Sheet 5 OriginalFiled Oct. 50, 1950 A a ex" BY c/lar/ United States Patent M FLEXIBLECOUPLINGS Charles W. Belden and Harley E. Northrop,

- Westfield, N. Y.

11 Claims. (Cl. (M -9),

This invention relates to couplings of the class for coupling togetherrotary shafts that are out of axial alignment, and commonly known asflexible couplings.

There is a known type of flexible coupling which cornprises in general,two parts having the general form of spur gears, each mounted on one ofthe shafts, and a third common part in the general form of an outer ringgear, the teeth of each spur gear being meshed with internal teeth onthe ring gear; and the present invention is an improved coupling of thistype. I Such couplings are usually referred'to as gear type couplings;because the teeth on the said parts may be conveniently formed bygear-tooth cutting machinery, and because the parts considered aloneresemble toothed gears. In fact, however, the characteristic action ofgears, that is, a pitch circle of one rolling on a pitch circle of theother, is entirely absent in the coupling; all of the teeth and toothspaces of the said outer toothed part of the coupling being at all timesintermeshed with all of the .teeth and tooth spaces of the said twoinner parts in the nature of spline connections.

Axial misalignment of the shafts to. be coupled will be present whentheir axes are at anangle to. each other; or when they are parallel butoffset laterally, one from the other; or, when they are at an angle andalso offset. When two shafts, in axial misalignment of either, of saidtypes, are coupled by such a coupling the medial plane of the inner gear(or gears) is at an angle to the medial plane of the outer gear (as willbe shown hereinafter), that is, the inner gear is tipped angularlywithin .the outer gear, and in the absence of special provisions theteeth of the inner gear will .bind .in..the teethof the: outer gear.This would present noQdifficult problem if the angleof shaftmisalignnint'could be selectedor predetermined .and be always the same;because itfcould be solved simply by providingsufiicientclearancebetween the teeth of the two meshed gears. But the couplingto be practicable .and commercial must be adapted to couple shafts of'different misalignment angles in different installations; and in. factthe actual angleis almost always unknown. An angle ofmisalignment'greater'than 3 is vvisibly appar- -.ent, and can usually bepartially corrected or reduced,

so that in general a couplingwi ll have sufficient range of adaptabilityif it can couple shafts at all angles from 0 to In toothed gear practicegenerally, itis desirable "to provide a, small cleanance between themeshed teeth;

and such clearance is also desirable between the teeth 'in a gear typecoupling The small amount of lost mo: tion introduced by suchclearanceis harmless and negligible.

However, in a'gea'r type coupling, if the teeth are given enoughclearancefto allow the inner gear to be tipped enough, as aforesaid tocoupleshafts at an angle of misalignment as greatas 3', then, when'usedto couple shafts at a lesserangle of misalignment, with the inner2,841,966 ii aizented July 8, 1958 IQQ countervailing provisions, thelost motion is thereby made so great as to be properly described asback-lashf; that is, an amount of lost motion that permits the teeth tovibrate back and forth in the tooth spaces accompanied by discontinuousor intermittent transmission or torque through them which is not onlyobjectionable in a coupling but in many cases is damaging to thecoupling or to apparatus driven by it.

It has been proposed to give the teeth a special form to permit saidtipping of the gear; but in all prior cou plings, if the special form ofteeth permits the gear to tip as aforesaid and without back-lash for onedegree of misalignment and tipping, it will cause binding or introduceback-lash at other degrees. So far as is now known, no form of tooth hasheretofore been devised which will obviate these defects.

Perhaps the most completely developed prior coupling of this type is onein which the inner gears are spherical gears, that is, have teeth cutwith respect to a spherical pitch surface; but as will appearhereinafter, a spherical gear does not solve the double problem of nobinding and no back-lash.

The objects of the invention are:

To provide generally an improved coupling of the type referred to, bywhich shafts at any angle of misalignment from 0 to 3 or higher ifwanted, can be coupled and driven without binding and without back-lashin the coupling.

To provide for a coupling of the type referred to, an improved shape oftooth at the aforesaid spline connection of the parts by which back-lashor binding as referred to, may be obviated.

Other objects will become apparent to those skilled in the art to whichthe invention appertains. y

The actual invention is that set forth in the appended claims. 1

The preferred embodiment of the invention fully described herein is acoupling of the type referred to, and comprising an outer ring gear withinternal teeth preferably parallel to its axis; and an inner geartherteeth of which, on the opposite sides of a medial plane of the gear,

, converge rectilinearly toward the gear axis and rise from gear tippeda. lesser amount, and' in the absence of opposite cone surfaces whosebases are in the medial plane and whose apexes are in or near the gearaxis.

The teeth of the inner gear are preferably cut from ablank by a gearcutting hob, with generating relative motion of the hob and blank, whichmakes the faces of the teeth generally of involute form, although theinvolute shape of the faces is incidental and not essential.

The teeth, may be considered as having a chosen pressure angle, as inthe case of ordinary gears as such.

The maximum angular displacementof the shafts to be coupled which may beencountered in practice may also be chosen.

The pitch diameter of the gear may also be chosen, as represented by acircle on the teeth at their middle between root and tip.

Given the maximum angle of misalignment and the pressure angle and thepitch diameter, the cone angle and other factors may be determined froma formula to be described by which a coupling can be made that will haveno back-lash or binding at all shaft misalignment angles from zero tothe chosen maximum angle.

As will be referred to a maximum shaft misalignment angle of 3 willsuifice for most installations but as will be found hereinafter,misalignment angles up to or even greater than 6 are possible with theinvention without back-lash or binding.

The invention is fully disclosed in the following description taken inconnection with the accompanying drawings, in which:

is :1 longitudinal sectional view of a coupling embodying the inventionin one form and showing two shafts coupled together without misalignmentfor simplification;

Fig. 2 is an end elevational view of the coupling of Fig. 1;

Fig. 3 is a fragmentary view similar to a part of Fig. 1 illustratingparts as they appear when one of the shafts is at an angle ofmisalignment with respect to the other;

Fig. 4 is a diagrammatic view illustrating methods of cutting teeth onan inner gear element of Figs. 1 to 3;

Fig. 5 is a fragmentary view to enlarged scale of an upper part of Fig.1 illustrating meshed teeth on an outer and an inner gear element ofFig. 1;

Fig. 6 is a view illustrating the teeth of Fig. 5 as viewed from above;

Fig. 7 is a View illustrating the teeth of Fig. 5 as viewed from theend;

Fig. 8 is a cross sectional view of the teeth of Fig. 5 taken from theplane 8-8 of Fig. 5;

Fig. 9 is a cross sectional view from the plane 9-9 of Fig. 1;

Figs. 10 and 11 are views similar to Figs. 8 and 5, but illustratingmeshed teeth of the inner and outer gears when the inner gear is tippedwith respect to the outer gear;

Fig. 12 is a view similar to Fig. 1 illustrating another embodiment ofthe invention;

Figs. 13, 14, 15 and 16 are views illustrating the form of Fig. 1diagrammatically and showing the positions taken up by parts thereofunder different conditions of shaft misalignment;

Fig. 17 is a diagrammatic view illustrating another embodiment of theinvention;

Figs. 18 to 23 are views similar to Figs. 5, 6, S and 10 butillustrating teeth of the prior art; and,

Fig. 24 is a view similar to Fig. 4 illustrating a modification of theinvention hereof.

Referring to Fig. 1, there is shown at 1 and 2, two shafts coupledtogether by a flexible coupling embodying the invention. Forsimplification, the shafts are shown with their axes 3-4 in alignment. Acoupling hub member 5 is mounted on the end of the shaft 1 by a key 6and set screw 7. A hub member 8 is mounted on the shaft 2 by a key 9 andset screw it the two hub members being preferably alike and mountedreversely on the shafts. v

On the hub member 5 is an annular rib 11 on the pheriphery .of which aregear teeth 12 to be described,

the rib constituting what may be referred to as a disclike gear body andthe rib and teeth as an inner gear 13, The hub member 8 has a like rib14 and teeth 15 constituting an inner gear 16.

Surrounding the inner gears 13 and 16 is a tubular sleeve 17 on theinner wall of which are formed at one end portion elongated teeth 13meshed with the inner gear teeth 12 and at the other end portion,elongated teeth 19 meshed with the inner gear teeth 15; and the sleeve17 and its teeth 18 and 13 may be referred to as an outer gear 20.

The teeth 12-15 of the inner gears 13 and 1'6 fit the tooth spaces ofthe outer gear 20 in such manner that the outer gear is supportedthereon, see Fig. 9.

At the opposite ends of the hubs 5 and 8 they have cylindrical surfaces21 and 22. Surrounding these surfaces but spaced radially therefrom asat 23-24 are annular end plates 25 and 26 mounted on the ends of thesleeve 1'7 by screws 27-27.

The teeth 18-19 of the outer gear 20 terminate short of the ends of thesleeve 17 leaving annular grooves 28-29 between the plates 25-26 and theteeth 13-19.

Annular seals 30-31 of rubber preferably of a kind resistant to chemicalaction of oil, for example Neoprene, are provided between the saidcylindrical surfaces 21-22 of the hubs and the sleeve 17. They compriseouter annular beads 32-33. hottoming .inthesaidgrooves 28-29, andclamped between the rings 25-26 and the ends of the teeth 18-19 andthereby effecting seal with the sleeve 17.

The seals have annular flexible skirts 34-35 inclined inwardly radiallyand inwardly axially, terminating in annular beads 36-37 encircling thehub surfaces 21-22. Coiled springs 38-39 of the annular garter springtype encircle the beads 36-37 and constrictingly hold them upon thesurfaces 21-22 to effect seal thereat.

A sealed chamber 40 is thus provided in which a quantity of lubricatingoil is entrapped and sealed and thrown outwardly into an annular body ofoil on the inner side of the sleeve 17 by rotation of the parts in use,flooding and lubricating the meshed teeth.

The flexibility of the seal skirts 34-35 permits angular misalignment ofthe shafts 1-2 and tipping of the hubs 5-8 (to be referred to) whilemaintaining the seal.

The axially inner ends of the seal beads 36-37 are spaced from the ribs11-14 providing opposite annular pockets 43-44 in the ribs, allowingfreedom of the outer gear 20 to float andshift axially relative to theinner gears 13-16 without contacting the beads 36-37 and the extent ofthe shifting is limited or stopped in either direction by abuttingcontact of the teeth 12 and 15 with the outer beads 32-33.

Oil may be introduced into the chamber 40 after assembly of the couplingwith the shafts, through a screw plug 45 in the wall ofv the sleeve 17.

In operation, the shaft 1 when rotating .drives the inner gear 13; itsteeth 12 meshed with the teeth 18 of the outer gear 20 drive the latter;the teeth 19 of the outer gear meshed with the teeth 15' of the innergear 16 drive the latter; the inner gear 16 drives the shaft 2. Theparts are shown .in Fig. l with the shafts: 1 and 2 in axial alignment.

In Fig. 3, the shaft 1 is ,shown withits axis 3 at an angle ofmisalignment, a, with respect to the axis of the shaft 2 (not shown) andthe inner gear 13 is shown at the corresponding tipped angle withrespect to the outer gear 20 as the parts would'be in practice in anillustrative case; and the following description explains thecoupleddrive and its property of driving without back-lash or binding at allsuch angles of misalignment.

The teeth on the inner gears, for example the teeth 12 on the inner gear13 are cut from a solid blank as illustrated diagrammatically in 'Fig.4.

A circular blank 46 is shown with its periphery bevelled in oppositedirections from its medial plane 47, as at 48-49, so that the surfaces48-49 lie on opposite cones 50-51, having the medial plane 47 as theircommon base, and having their apices 52-53 in the axis of the blank.

The angle, b, between the side of the cone and the axis 54 willhereinafter be referred to as the cone angle. A helical hob 55 isrotated and fed parallel to the side of the cone 50 along the line 56cutting the blank from the right face as viewed in Fig. 4 to the medialplane of the blank, and then a hob 55A is. fed parallel to the side ofthe cone 51 along the line 57 cutting the blank from the left face tothe medial .plane 47. Alternative methods will be referred to later.

The blank is concurrently rotated on its axis 54 at a siutable speed forthe hob so that the hob cuts generated teeth with involute faces, in thesame and well known manner as ordinary involute gear teeth are cut andgenerated on gears that are to .beused as gears.

The teeth thus made will have the form shown in Figs. 5 to 8, where oneof them 12 is shown .to enlarged scale meshed with .a tooth space 58 .ofthe outer gear teeth 18.

The involute faces of the teeth IZindicated at59, Fig. 7, will taperfrom the root toward the tip and may 'be considered as having a pressureangle, as if they were to be used as ordinary rolling gear teeth, thepressure angle having been preselected by the shape or angle of thehelical hob teeth.

In Figs. 5 and 8, the tooth 12 of the inner gear 13 is shown in thecondition of the parts of Fig. 1 without misalignment angle, andtherefore with the gear not tipped as referred to, and, as seen, thetooth face (toward the observer in Fig. 5) is in two halves 6tl-61meeting in a dihedral edge or corner 62 at the medial plane; and theopposite face (Fig. 6) likewise has two halves 63-64 meeting in adihedral edge 65. As viewed in Fig. 5, all parts of the tooth sloperectilinearly from the medial plane toward the opposite ends of thetooth, at the cone angle b.

As will be evident, the bottoms of the tooth spaces Will define a conesurface having the preselected cone angle b; and this is indicated bythe angle b in Fig. 5.

The teeth 18 of the outer gear 20 are cut by the usual internal gearcutting method and preferably parallel to the axis, at a pressure anglesuch that the teeth 12 of the thickest part of the inner gear teeth atthe dihedral angle edge 62-65 conform to and substantially fit the toothspaces 58 of the outer gear teeth as shown in Fig. 9.

The faces of the tooth in the direction parallel to the gear axis andparallel to the teeth spaces 58 of the outer gear, are approximatelyrectilinear as shown in Fig. 8 for the section plane 8-3 of Fig. 5; andthis illustrates one of the most important features of theinvention tobe more fully described; but here it is pointed out that as illustratedin Fig. 8, even if the tooth 12 fits the tooth space 58 so intimatelythat the points 66-67 on the said dihedral corners 62-65 of the toothare in actual contact with the tooth faces 68-69 of the teeth lili, thenbecause of the cone angle at which the teeth are formed, the faces 69,61, 63, 6d of the teeth 12 all incline inwardly away from the toothfaces or sides altof the teeth of the outer gear in rectilineardirections, at both sides of the dihedral edge points 66-67.

Referring now to Fig. 9, in which the inner gear 13 is shown as in Fig.1, without being tipped due to shaft misalignment, and with its teeth 12meshed in the tooth spaces 53 between the teeth 1% of the outer gear 23,it is convenient to designate the top, bottom, and sides of the innergear, as viewed, by the characters A, B, C and D.

In this tin-tipped position of the inner gear 13, the teeth 12 at allfour positions A to D, will be in the relation to the outer gear teethspaces, as illustrated in Figs. 5 to 8. The teeth 12 can be made, aswill be understood, by setting the hob 55, Fig. 4, at a suitable cuttingdepth, so that in Figs. 5 to 8, the dihedral edges as and 65 of theinner gear 13 will be in actual contact with the sides 6:: and 69 of theteeth 13 of the outer gear, that is, without any clearance therebetween.All of the teeth 12 of the inner gear will mesh with and engage anddrive the teeth 18 of the outer gear.

When the shafts are at a misalignment angle a, as re ferred to, theinner gear 13 is tipped within the outer gear 20 as in Fig. 3. In Fig.9, the top A is then nearer to the observer, the bottom B farther awayfrom the observer; and the parts C and D are rocked on a horizontal axis167, rocking or twisting the inner teeth 12 on that axis.

In Fig. 3, this rocked or twisted position of the tooth 12 at theposition C is shown in dotted lines and as seen it lies diagonally inthe tooth space 555 of the outer gear 20; and this twisted position isalso shown more clearly in Fig. which is drawn to correspond to theuntwisted position of Fig. 8.

As the inner gear is thus tipped, the tooth which is at the position C(or D) of Fig. 9 goes from the condition of Fig. 8 to that of Fig. 10.

Assuming that the tooth was in actual contact at points such as 66-67 ofthe dihedral edges na es as shown in 6 Fig. 8, it will nevertheless befree to twist to the position of Fig. 10, without binding. In going fromFig. 8 to Fig. 10, the point 67 may be considered as pivoting or movingin a circular are around the point 66,. and therefore as introducing aslight amount of clearance at the point 67.

The maximum angle through which the tooth 12 can twist in this mannercan be made to be at least as great as the maximum angle of shaftmisalignment to be encountered, and causing the twist, by providing asuitable cone angle as will be explained.

in Fig. 10, the tooth 12 is shown as twisted through the aforesaid anglea of Fig. 3.

The foregoing total possible tipping of the gear 13 and twisting oftooth 12 at positions C and D, assumes that the gear 13 is free to tipwithout binding at any point.

This will be true for the teeth 12 at positions A and B, Fig. 9, becausetheir arcuate movement around the axis 1167 upon tipping of the gear onthat axis will be generally parallel to the tooth spaces 58 of the outergear in which they are meshed, and they will take up positions such asshown in Fig. 11 for the position A.

This arcuate movement will have a component toward the axis 167 and thedihedral edges of the tooth will be withdrawn slightly, radially, out ofthe tooth spaces 58 and not be in actual contact at said positions A andB.

At positions of Fig. 9 between positions A and D (and similarly betweenpositions D-B and 13-0 and C-A) tipping of the inner gear and rockingits teeth around the axis 167 gives the teeth a component of movement toward the observer in Fig. 9 and also a component vertically downward asviewed in Fig. 9 which latter tends to make the teeth 12 engage and bindon the outer gear teeth ti; and limit the said tipping angle (assumingthat the inner and outer gear teeth were in actual contact at thedihedral edges 5?. and in the non-tipped position).

it can be demonstrated by trigonometry that the point between positionsA and D for example, at which this binding tendency is greatest, dependsupon the pressure angle chosen for the teeth, being nearer to theposition D for larger pressure angles and farther away from D forsmaller pressure angles approaching a position midway between A and Dfor zero pressure angle.

The teeth 12 will therefore be cut to provide relief to permit tippingof the inner gear through the maximum angle as aforesaid, and this isdone by simply setting the hob to cut deeper.

A very slight amount of such relief cutting is needed for this purpose,less being required for teeth of large pressure angle than for teeth ofsmall pressure angle.

After such relief cutting is provided, the teeth 12 will be at actualcontact with the teeth 18 in said intermediate positions when the gearis fully tipped; but the teeth 12 will be thinner at the dihedralcorners 62-65 in the medial plane, and this tends to introduce clearancethereat. When the inner gear therefore is in the non tipped condition,this clearance will appear at points 66-67, Fig. 8, and at all of theteeth around the gear; and when the gear is in the fully tippedcondition, clear ance will appear at the points 66-67, Fig. 10.

But this clearance is still in all cases negligibly small, being less infact that would be occupied by a lubricating oil film, as will be shown,and will introduce no backlash.

Since it is contemplated that the teeth are to be lubricated by oil, andsince if the teeth were cut as above described, the clearance at allteeth and in all positions is less than the thickness of an oil film,the hob must now he set to out still deeper to provide clearance enoughfor oil film to form and be maintained on the teeth.

in the foregoing for description purposes, and as stated, the teeth 12on the inner gear 13 were considered as they would be if out so as to bein actual contact all around the gear at the dihedral edges 62-65 (Figs.5 to 8) in the non-tipped position of the inner gear; and

2 then considered as further cut to provide relief for the sake of theintermediate positions (between A and D etc); and then further cut toprovide oil film clearance. In practice, of course, all of this cuttingwould be done at one operation with a single depth setting of the hob.

When the inner gear is tipped through the maximum angle, correspondingto the maximum shaft misalignment angle, that may be encountered, thegears drive at the teetl that are in said intermediate positions,between A and C etc., because the clearance is then the least at thosepositions.

For smaller and smaller angles of misalignment and less and less tippingof the inner gear, the position around the gear at which driving occurs,spreads over more and more teeth both clockwise and counterclockwisefrom said position, taking in more and more teeth until at zero tippingang e, it extends all the way around the gear and driving occurs on allof the teeth and the clearance is then at the maximum.

lust how little the aforesaid clearance is, including that necessary toprevent binding at the said intermediate positions plus enough toprovide room for oil, can be ascertained from the following deductions;which also provide data for making a coupling free from back-lash orbinding as contemplated by the invention.

To design and make a coupling embodying the invention and having theabove described advantages, certain assumptions will be made as follows.

Assume that the maximum shaft misalignment angle to be encountered willbe 3.

The maximum tipping angle of the inner gear and the maximum twist angleof the inner gear tooth as in Fig. will then be 3.

The tendency to bind at the four intermediate positions between A and D(D and B etc.) and for which relief is provided, will be greater forsmall pressure angles of the inner gear teeth than for large, and,corresponding to spur gear tooth practice the pressure angle may be inthe range from 14 to 30 and will be assumed here to be 25.

The said tendency to bind will also be greater for large inner geardiameters than for small diameters and a gear of 4" diameter will beassumed, the diameter being taken at a point on the gear teethcorresponding to the pitch diameter of ordinary spur gear teeth and at,say, the middle of the teeth radially considered.

Let G equal the intermediate point for example the point between A andD, Fig. 9, at which maximum interference and binding tends to occur,when the gear tips the maximum due to misalignment angle, G beingmeasured in degr cs of angle from the position A.

Let H equal the maximum shaft misalignment angle to be encountered; andit therefore also represents the maxi mum angle of twist of the geartooth as in Fig. 10.

Let l equal the pressure angle of the inner gear teeth.

Let X equal the amount of metal in inches that must be removed. from theside of the tooth to prevent binding at the point G at maximum tippingof the gear.

Let PD equal the pitch diameter of the gear.

Let Y be a constant equal to the cotangent of the pres sure angle andhaving values as follows.

For pressure angle:

14 /2 Y equals 3.86 Y equals 2.74 Y equals 2.14 Y equals 1.74

X equals {[cos G-(cos G. cos H)] sin (GI)l PD F equals HXY G equalsSolving for G, F and X in an assumed case of pressure angle I equal to25; Y equal to 2.14; H equal to 3; and PD equal to 4":

G equals 57.5 F equals 6.42 X equals .0017

The clearance will be maximum at .0017" in the nontipped position of theinner gear at 0 misalignment; the clearance will be zero at the 57.5position G betav A and D for maximum misalignment of 3, and iencc atthis point enough clearance must be added to contain oil film forlubrication, say .002". This added oil film clearance will also appearas added to the clear- 83. of 33017 for no-angle of misalignmentconditions; it ing the maximum clearance at any condition .0037".

This small clearance, filled as it is with lubricant oil is too small tocause any back-lash lost motion even at the maximum clearance conditionof no misalignment angle, and is of course, as shown, even less at allmisalignment angles, down to .002 at maximum misalignment angle. It isto be noted that in ordinary spur gear practice a clearance betweenteeth of .004" or even greater is provided, and will contain lubricant,and introduce no objectionable back-lash; and therefore of course theclearance of .0037" will introduce no objectionable baclolash in thepresent invention.

As stated hereinbefore perhaps the most fully developed coupling of thisgeneral class proposed heretofore is one in which an inner gear hasteeth cut like the teeth of a spherical spur gear; and the improvementof the instant invention over such prior couplings will here beexplained in connection with Fig. 19, 18, 20 and 21, which in the ordernamed, corresponds respectively to Figs. 5, 6, 8 and 10 above discussed.

In cutting teeth on the spherical gear 71, the hob travels on a circle(instead of along two rectilinear lines at an angle, such as lines sss7, Fig. 4). The faces of the tooth it? will therefore be convexlycurved as at 72-73 in l8 and 20. If the teeth 70 are cut of suchthickness, tiat when the inner gear is in the aforesaid non-tippedposition, Fig. 19, and the tooth 70 in the tooth space 76 of the outergear is without twist, and so that there will be little or no clearanceor back-lash, the tooth 76 will be substantially in contact with. theouter gear tooth faces at points 7'773, Fig. 20, which corre spond topoints 6ti-ti7 of Fig. 8.

in the present invention when the inner gear became tipped and the toothtwisted in position as described, the conditions at the inner gear teethchanged from Fig. 8 to Fig. 10. With the spherical gear tooth, thatwould correspond to going from Fig. 20 to Fig. 21. But as will be seenin Fig. 21, this would be impossible because of the convexity of thetooth faces 72- 75.

Assuming that the tooth face 72 remains in contact with the outer geartooth face 74, the tooth in effect rocks on the face 7tand the point ofcontact '77, Fig. 20, shifts to 77A in Fig. 21, and the other face 73 ofthe tooth would have to overlap into the metal behind th tooth face, 75,as indicated by the dotted line 1 9, and this is impossible.

Thus, if the tooth 72B fits the tooth space 76 without back-lash beforegear tipping, the inner gear cannot tip at all to allow for shaftmisalignment as explained hereinbefore.

In order to allow it to tip, and to allow the tooth to twist, the tooth70 must be cut thinner, for example as in Fig. 22, where as shown itwill all be within the tooth space 7 6.

Now even if the tooth is cut as thick as possible so as to be inactualcontact at points 77A and A as in Fig. 22, to eliminate back-lash atmaximum shaft misalignment and maximum gear tip and tooth twist, thenfor smaller angles of shaft misalignment and little tooth twist as inFig. 23, the thinness of the tooth 70 introduces 9 a large clearance asat 80 with attendant lost motion and back-lash.

Thus with the spherical inner gear, the coupling can only be designedfor a very limited range of shaft angle displacement without lost motionand back-lash.

The coupling of Fig. l is what may be called a double form, the outergear element or s1eeve17 being supported by and floating on the meshedengagement of two sets of teeth 18 and 19 with the teeth 12 and 15 oftwo inner gear elements 13 and 16 one on each of the shafts 1 and 2 tobe coupled.

In Fig. 13, this coupling is shown diagrammatically when the two shafts1 and 2 are substantially in axial alignment.

In Fig. 15, the shafts 1 and 2 are displaced at an angle to each otherand the outer sleeve 17 takes up an angular position, and part of theangle of shaft misalignment appears in the tipped angle of gear 13 andpart of it in gear 16.

In Fig. 14, one shaft 2, is at an angle to the other shaft 1, anddisplaced laterally with respect toit, so that all of the tipping angleis at the gear 13; and this case illus trates the importance of havingno back-lash in the nontipped condition of the inner gear 16, as well asin the tipped condition of the gear 13.

Fig. 16 illustrates the conditions when the two shafts, 1 and 2 areparallel but offset laterally, one from the other. Both gears 13 and 16are tipped with respect to the outer gear 17.

In Fig. 12 is illustrated a coupling in what might be called a singleform. An inner gear 13 having teeth 12 is mounted on a shaft 1 andsealed by a seal 30, substantiallyof the same construction as in Fig. 1.The outer gear teeth 18 are here on a sleeve 81 having a flange 82 bywhich it is secured by screws 83 to a flange 84 on a hub 85 mounted onthe other shaft, here 2A. An oil chamber 86 is provided within thesleeve 81 and supplied through a duct 87 closed by a plug 38.

The coupling of Fig. 12, as will be apparent, may be used with theshafts 1 and 2A in the cases illustrated in Figs. 13 and 14 for theshafts 1 and 2.

In Fig. 17, is shown diagrammatically an arrangement usingthe couplingof Fig. 12 as a universal joint construction in the line of two shaft 89and 90, offset laterally and at an angle to each other.

In Fig. 17, a coupling 91 is provided which may be like the coupling ofFig. 12, the outer gear teeth 18 being on a sleeve 31 connected to a hub85 on theshaft 90; and having an inner gear 13 with teeth 12 meshed withthe teeth 18.

A similar or like coupling 92 is mounted on the shaft 89, identified bythe same part numbers with the sufiix A.

The two inner gears 13 and 13A are connected together by a shaft 93. I

The couplings are lubricated as described for Fig. 12 and sealed byseals 30-30A which may be the same as hereinbefore described.

A universal joint of this construction-has the advantage that lubricantis not thrown out ofit by centrifugal force as in the case of many priorjoints, but is maintained thereby in an annular ring at the engaged gearteeth submerging them at all times.

It is believed that it will be apparent that the arrangement of Fig. 17may be used with at afts that are parallel but offset from each other;or, at an angle to each other and not offset.

To simplify the description of the process of Fig. 4, the blank 1-6 wasdescribed as having its periphery precut to the cone angle. This is notan essential step of the process. It is preferable for the periphery tobe cut at some angle or rounded at each side of the medial plane inorder that the tip surfaces of the teeth 94-95 (see Figs. and 11) willnot bottom in the outer gear tooth spaces when maximum tip of the innergear occurs, as

they might as indicated in broken line at 95A, Fig. 11, if for examplethe blank periphery had been cylindrical.

In the process of Fig. 4 aswill now be apparent, the helical hob 55 maybe moved to approach the blank as along the line 56 while another hob55A is approaching the blank along the line 57 at the same time but at adifferent point around the blank.

Or the hob 55 after approaching the blank and cutting along the line 56may be changed in direction and moved along the line 57 continuing tocut and finally leave the blank.

It is believed that, from the foregoing, it will be clear that a part ofthe invention of primary importance resides in providing teeth ontheinner gear of such form that a tooth may fit in a tooth space of theouter gear with no more clearance therewith than is necessary for an oilfilm, in ordinary gear practice, when the inner gear is not tipped, andthere is no shaft misalignment; and at the same time when the inner gearis tipped by shaft misalignment will allow the inner gear teeth to twistin the outer tooth spaces without binding.

Such teeth can be made most conveniently and efficiently by generatingthem as involute teeth with helical hob and feeding the hob so that thecut teeth conform generally. to the surfaces of two opposing cones whosecommon base is at the medial plane of the gear and whose apices are inthe axis of the gear, and for that reason the described process and theresulting gear are preferred.

In any of the above mentioned methods of cutting the teeth, for exampleand with reference to Fig. 4 it will, of course, be understood that thehob 55 may be fed in either direction alongthe line 56, that is, eithertoward or from the medial plane of the blank, the choice beingdetermined by factors of design of the machine driving and feeding thehob.

In Fig. 4, when considered as illustrating the movement of a hob alongthe rectilinear lines 56 and 57, these paths of movement meet at a point106, at which the lines of movement intersect.

However, in some cases, having in mind the design of a machine to driveand directionally feed the hob, it may be found advantageous. to go fromthe direction 56 to the direction 57 (or vice versa) with a curvedmovement. This is illustrated in Fig. 24. The path of movement 56proceeds rectilinearly to a point Hi7 and continues into the path 5'! ata point 108 and between the points 107 and 168 the path is curved,preferably circular, as at 109.

When this process is used, the dihedral angle corner or edge will not bea sharply designed edge, as in Fig. 5 at 52 for example, but will be aslightly rounded dihedral corner, or small area 62A as in Fig. 24-,departing from a sharp dihedral corner by a few ten thousandths of aninch; but for all practical purposes and as defined here, it is adihedral edge. Any clearance that might be introduced thereby may benegligibly small, and in any event is obviated by setting the hob to cutslightly less deep.

The above tooth cutting processes have been referred to the medial planeof the blank 46. It is not a necessary limitation that the medial planebe exactly midway between the faces of the blank or exactly midwaybetween the opposite ends of the teeth; nor that it be exactly at rightangles to the axis of the blank considered as circular; nor that theapex of the cone be exactly in the axis of the blank; as it is believedwill be understood.

While it is preferred to cut the teeth on the inner gears by a toothgenerating helical hob as described, it is believed that it will beapparent that they may be cut with a circular, disc-like, toothedmilling cutter having suitably formed teeth, and fed across the blankalong the cone-angle lines 56 and 57 of Fig. 4, without ass-Lose at anangle to the medial plane, which would make the teeth in generalcorrespond to helical gear teeth. It is believed that this will beunderstood without further illustration or description.

In such case the teeth would still be properly described as conformingin general to the surfaces of cones, whose apices are at opposite sidesof the blank.

in all cases, it is a characteristic of the teeth of the inner gear,that the bottoms of the tooth spaces between the teeth in the preferredpractice are caused to lie substantially on the surfaces of two oppositecones, having apices at opposite sides of the gear, by correspondinglyfeeding the cutter or cutters, but the advantages of the invention willnot be lost if the direction of feed is not strictly rectilinear asdescribed. Also, while the teeth of the outer gear are described aspreferably rectilinear and parallel to its axis, it will be apparentthat the advantages of the invention will not be lost if some curvatureis given to these teeth, concave or convex with respect to the axisthereof.

This application is a continuation of application Serial No. 192,954filed October 30, 1950.

We claim:

1. A flexible coupling for coupling a pair of rotary shafts, comprisingan outer gear element having a circular series of inwardly extendingteeth, and an inner gear element comprising a disc-like body portionhaving a like circular series of outwardly extending teeth on itsperiphery; the gear elements positionable with the outer gear elementsurrounding the inner gear element, and with the teeth of the gearelements in mutually meshed engagement; means by which one shaft maydrive the other through the tooth engagement, comprising connectingparts between the respective gear elements and shafts to cause them torotate respectively with the shafts; the teeth of the gear elementsconstructed so that the drive will occur without back-lash and Withoutbinding at the tooth engagement, when the rotational axes of the gearelements, due to the positions of the shafts, are at any angle of axialmisalignment, with each other in the range from zero degrees to a chosenpreselected maximum; the tooth construction of the outer gear elementcomprising teeth that extend substantially rectilinearly parallel to itsaxis; the tooth construction of the inner gear element comprising toothspaces between adjacent teeth having bottom surfaces disposed to definethe side surfaces of two geometrical cones having a common base in aplane of the body portion between its sides, and having cone apices inthe axis of the body portion spaced from the opposite sides thereof; andthe veth being involute teeth, and having a known pressure angle; andthe teeth being of greatest thickness at a portion thereof in the planeof the common cone base, and tapering therefrom in opposite directionstoward the sides of the body portion; and the angle of each cone betweenits axis and a side thereof being equal to the said preselected maximumangle of misalignment, multiplied by the value of the cotangent of thesaid known pressure angle.

2. A flexible coupling for coupling a pair of rotary shafts, comprisingan outer gear element having a circular series of inwardly extendingteeth, and an inner gear element comprising a disc-like body portionhaving a like circular series of outwardly extending teeth on itsperiphery; the gear elements positionable with the outer gear elementsurrounding the inner gear element, and with the teeth of the gearelements in mutually meshed engagement; means by which one shaft may dr''e the other 12 through'the tooth engagement comprising hub parts on therespective gear elements by which they may be connected respectively tothe shafts, to rotate therewith; the teeth of the gear elementsconstructed so that the drive will occur without back-lash and withoutbinding at the tooth engagement when the rotational axes of the shaftsare at an angle of misalignment with each other, in the range from Zerodegrees to a chosen preselected maximum; the

tooth construction of the outer gear element comprising teeth thatextend substantially rectilinearly parallel to the of the shaft to whichit is connected; the tooth construction of the inner gear elementcomprising tooth spaces between adjacent teeth having bottom surfacesdisposed to define the side surfaces of two geometrical cones having acommon in a plane of the body portion between its sides, and having coneapices in the axis of the body portion spaced from the opposite sidesthereof; and the teeth being involute teeth, and having a known pressureangle; and the teeth being of greatest thickness at a portion thereof inthe plane of the common cone base, and tapering therefrom in oppositedirections toward the sides of the body portion; and the angle of eachcone between its axis and a side thereof being equal to the saidpreselected maximum angle of misalignment, multiplied by the value ofthe cotangent of the said known pressure angle.

3. A flexible coupling for coupling a pair of rotary shafts, comprisinga pair of inner gear elements each comprising a disc-like body portionhaving a circular series of outwardly extending teeth on its periphery;and having hub portions by which they may be connected respectively toadjacent confronting end portions of the shafts and rotate therewith andbe adjacent to each other; anouter gear element having a circular seriesof inwardly extending teeth and formed to surround both inner gearelements with the teeth of the outer gear element in mutually meshedengagement with the teeth of both inner gear elements, and to besupported by the tooth engagement; whereby one shaft may drive the otherthrough the tooth engagement; the teeth of the gear elements constructedso that the drive will occur without back-lash and. without binding atthe tooth engagement when, due to the positions of the shafts, the axisof either inner gear element is at an angle of misalignment with theaxis of the outer gear element in the range from zero degrees to achosen preselected maximum; the tooth construction of the outer gearelement comprising teeth that extend substantially rectilinearlyparallel to the axis of the circular series of teeth thereon; the toothconstruction of each of the inner gear elements comprising tooth spacesbetween adjacent teeth having bottom surfaces disposed to define theside surfaces of two geometrical cones having a common base in a planeof the body portion between its sides, and having cone apices in theaxis of the body portion spaced from the opposite sides thereof; and theteeth being involute teeth, and having a known pressure angle; and theteeth being of greatest thickness at a portion thereof in the plane ofthe common cone base, and tapering therefrom in opposite directionstoward the sides of the body portions; and the angle of each conebetween its axis and a side thereof being equal to the said preselectedmaximum angle of misalignment, multiplied by the value of the cotangentof the said known pressure angle.

4. A flexible coupling for coupling a pair of rotary elements,comprising a circular inner gear element having outwardly extendingteeth; a circular outer gear element having inwardly extending teeth;the two gear elements positionable with the outer gear elementsurrounding the inner gear element and with the teeth of the gearelements in mutually meshed engagement; means by which one rotaryelement may drive the other through the tooth engagement comprisingconnecting par-ts between the respective gear elements and rotaryelements to cause them to rotate respectively with the rotary elements;the teeth of the gear elements being formed so that the drive will occurwithout back-lash or binding at the tooth engagement when the rotationalaxes of the gear elements, due to the positions of the rotary elements,are at an angle of misalignment with each other in the range from zerode grees to a preselected maximum; the tooth form of the outer gearelement being such that the teeth extend longitudinally in the directionof the gear axis; the tooth form of the inner gear element being suchthat each tooth has portions extending outwardly at right angles to thesurface of a geometrical cone coaxial with the inner gear element.

5. A flexible coupling for coupling a pair of rotary elements,comprising a circular inner gear element having outwardly extendingteeth; a circular outer gear element having inwardly extending teeth;the two gear elements positionable with the outer gear elementsurrounding the inner gear element and with the teeth of the gearelements in mutually meshed engagement; means by which one rotaryelement may drive the other through the tooth engagement comprisingconnecting parts between the respective gear elements and rotaryelements to cause them to rotate respectively with the rotary elements;the teeth of the gear elements bing formed so that the drive will occurwithout back-lash or binding at the tooth engagement when the rotationalaxes of the gear elements, due to the positions of the rotary elements,are at an angle of misalignment with each other in the range from Zerodegrees to a preselected maximum; the tooth form of the outer gearelement being such that the teeth extend longitudinally in the directionof the gear axis; the tooth form of the inner gear element being suchthat each tooth has portions extending outwardly at right angles to thesurface of a geometrical cone coaxial with the inner gear element, and,considered as an ordinary gear tooth, has a known pressure angle, andthe cone angle between the cone surface and its axis is equal to thesaid maximum angle of misalignment multiplied by the value of thecotangent of the pressure angle.

6. A flexible coupling for coupling a pair of rotary elements,comprising a circular inner gear element having outwardly extendingteeth; a circular outer gear element having inwardly extending teeth;the two gear elements positionable with the outer gear elementsurrounding the inner gear element and with the teeth of the gearelements in mutually meshed engagement; means by which one rotaryelement may drive the other through the tooth engagement comprising hubparts on the respective gear elements by which they may be connectedrespectively to the rotary elements to rotate therewith; the teeth ofthe gear elemens being formed so that the drive will occur withoutback-lash or binding at the tooth engagement when the rotational axes ofthe gear elements, due to the positions of the rotary elements, are atan angle of misalignment with each other in the range from zero degreesto a preselected maximum; the tooth form of the outer gear element beingsuch that the teeth extend longitudinally in the direction of the gearaxis; the tooth form of the inner gear element being such that eachtooth has por tions extending outwardly at right angles to the surfaceof a geometrical cone coaxial with the inner gear ele ment.

7. A flexible coupling for coupling a pair of rotary elements,comprising a circular inner gear element having outwardly extendingteeth; a circular outer gear element having inwardly extending teeth;the two gear elements positionable with the outer gear elementsurrounding the inner gear element and with the teeth of the gearelements in mutually meshed engagement; means by which one rotaryelement may drive the other through the tooth engagement comprising hubparts on the respec tive gear elements by which they may be connectedrespectively to the rotary elements to rotate therewith; the teeth ofthe gear elements being formed so that the drive will occur withoutback-lash or binding at the tooth engagement when the rotational axes ofthe gear elements, due to the positions of the rotary elements, are atan angle of misalignment with each other in the range from zero degreesto a preselected maximum; the tooth form of the outer gear element beingsuch that the teeth extend longitudinally in the direction of the gearaxis; the tooth form of the inner gear element being such that eachtooth has portions extending outwardly at right angles to the surface ofa geometrical cone coaxial with the inner gear element, and, consideredas an ordinary gear tooth, has a known pressure angle, and the coneangle between the cone surface and its axis is equal to the said maximumangle of misalignment multiplied by the value of the cotangent of thepressure angle.

8. A flexible coupling for coupling a pair of rotary elements,comprising a pair of inner gear elements each having outwardly extendingteeth; an outer circular gear element having inwardly extending teethand formed to surround both inner gear elements with the teeth of theouter gear element in mutually meshed engagement with the teeth of bothinner gear elements, and to be supported by the tooth engagement; meansby which one rotary element may drive the other through the toothengagement comprising hub parts on the respective inner gear elements bywhich they may be connected respectively to the rotary elements torotate therewith; the teeth of the gear elements being formed so thatthe drive will occur without back-lash or binding at the toothengagement when the rotational axis of either of the inner gearelements, due to the positions of the rotary elements, is at an angle ofmisalignment with the axis of the outer gear element in the range fromzero degrees to a preselected maximum; the tooth form of the outer gearelement being such thatrthe teeth extend longitudinally in the direction of the gear axis; the tooth form of the inner gear elements beingsuch that each tooth has portions extending outwardly at right angles tothe surface of a cone coaxial with the inner gear element.

9. A flexible coupling for coupling a pair of rotary elements,comprising a pair of inner gear elements each having outwardly extendingteeth; an outer circular gear element having inwardly extending teethand formed to surround both inner gear elements with the teeth of theouter gear element in mutually meshed engagement with the teeth of bothinner gear elements, and to be supported by the tooth engagement; meansby which one rotary element may drive the other through the toothengagement comprising hub parts on the respective inner gear elements bywhich they may be connected respectively to the rotary elements torotate therewith; the teeth of the gear elements being formed so thatthe drive will occur without back-lash or binding at the tooth engagement when the rotational axis of either of the inner elements, due tothe positions of the rotary elements, is at an angle of misalignmentwith the axis of the outer gear element, in the range from zero degreesto a preselected maximum; the tooth form of the inner gear elementsbeing such that each tooth has portions extending outwardly at rightangles to the surface of a cone coaxial with the inner gear element;and, considered as an ordinary gear tooth, has a known pressure angle,and the cone angle between the cone surface and its axis is equal to thesaid maximum angle of misalignment multiplied by the value of thecotangent of the pressure angle.

10. A flexible coupling comprising an outer gear element having aplurality of inwardly extending teeth, and an inner gear element havinga disc-like body portion with a like plurality of outwardly extendingteeth; the gear elements telescoped together with their teeth mutuallymeshed and constructed to be drivingly connected respectively with apair of rotary shafts; the gear elements having each a construction suchthat one shaft may rotatively drive the other through meshed toothengagement without back-lash and without binding at the tooth engagementwhen the shaft axes are at any angle of misalignment with each other inthe range from zero degrees to a chosen preselected maximum angle; theconstruction of the outer gear element comprising teeth and tooth spacesthat extend substantially rectilinearly parallel to the axis of theshaft with which it is connected; the construction of the inner gearelement comprising tooth spaces having bottom surfaces disposed todefine the surfaces of two geometrical cones having a common basesubstantially in a plane of the body portion between the sides thereofand having apices substantially in the axis of the body portion andspaced from the opposite sides thereof; and each tooth being an involutetooth and having a known pressure angle; and each tooth being ofgreatest thickness at a portion in the plane of the common cone base andtapering therefrom in opposite directions toward the sides of the bodyportion; and the angle of said cone between its axis and a side thereofbeing equal to the said preselected maximum angle of shaft misalignmentmultiplied by the value of the cotangent of the said known pressureangle.

11. A flexible coupling comprising an outer gear element having aplurality of inwardly extending teeth, and an inner gear element havinga disc-like body portion with a like plurality of outwardly extendingteeth; the gear elements telescoped together with' their teeth mutuallymeshed and constructed to be drivingly connected respectively with apair of rotary shafts; the gear elements having each a construction suchthat one shaft may rotatively drive the other through meshed toothengagement without back-lash and without binding at the tooth engagementwhen the shaft axes are at any angle of mis- 1&5 alignment with eachother in the range from zero degrees to a chosen preselected maximumangle; the construction of the outer gear element comprising teeth andtooth spaces that extend substantially rectilinearly parallel to theaxis of the shaft with which it is connected; the con,- st uction of theinner gear element comprising tooth spaces having bottom surfacesdisposed to define the surfaces of two geometrical cones having a commonbase substantially in a plane of the body portion between the sidesthereof and having apices substantially in the axis of the body portionand spaced from the opposite sides thereof; and each tooth havingconvexly curved outwardly extending faces having a known pressure angle;and each tooth being of greatest thickness at a portion in the plane ofthe common cone base and tapering therefrom in opposite directionstoward the sides of the body portion; and the angle of said cone betweenits axis and a side thereof being equal to the said preselected maximumangle of shaft misalignment multiplied by the value of the cotangent ofthe said known pressure angle.

References Cited in the file of this patent UNITED STATES PATENTS2,303,813 Barcus Dec. 1, 1942 2,496,702 Dykman et al. Feb. 7, 19502,682,760 Shenk July 6, 1954

